Overview and Background

Students will see how to find the area of a hexagon based on their pre-existing knowledge of finding the area of a triangle.

The purpose of this activity is for students to see a hexagon is made of 6 equivalent triangles and to find the area of the hexagon they just need to find the area of one triangle then multiply by 6.

Skills Learned (Standards):

CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

CCSS.Math.Content.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CCSS.Math.Content.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Lesson Plan and Activity

To introduce the topic show students a clip from Sonny With a Chance (season 1, episode 5). In it Sonny has been doing bad at math and she has a big geometry test coming up. In one scene Zora tries to explain geometry with a model. She says that a hexagon is made up of six triangles. The model has six triangles, each a different color, that are stuck together to form a hexagon. She pulls one triangle off and explains that if you find the area of one triangle you can find the area of the hexagon. The clip can be found here: https://www.youtube.com/watch?v=dXHdXpd3Te4.
Show students this printed model that is similar to the model used in the television show. You can print just one copy to pass around or have several for students to play with.
Have students prove that this is a regular hexagon.
Ask students to find the area of the hexagon.
Ask what other shapes they can make using only equilateral triangles. Can they make a triangle, a rhombus, some other shape? Then find the area of each of these shapes.

Skills Learned

Area of Triangles
Area of Geometry
Pythagorean Theorem

Duration of Lesson

One Day

Preparation

For this activity students should be familiar with hexagons and equilateral triangles and know how many degrees are in each. Students should also know how to find the area of an equilateral triangle and The Pythagorean Theorem.

Rubric and Assessment

Here is a sample rubric to use with this activity.

Question 3
Sum of interior angles of hexagon=720 (1)
Each angle = 120 (1)
Angles in equilateral triangles = 60 (1)

Question 4
Draw perpendicular (1)
Perpendicular splits side length in half (1)
Using Pythagorean Theorem to find height (2)
Area of triangle (1)
Area of hexagon (1)

Question 5
Make triangle and find area (2)
Make rhombus and find area (2)
Make other shape and find area (2)

Total 15

References

If students need a refresher on how to find the area of an equilateral triangle they can watch the Khan Academy videos on these topics.

https://www.khanacademy.org/math/geometry/basic-geometry/advanced-area-with-triangles/v/area-of-an-equilateral-triangle.

For a review of how to find the angles in a regular polygon students can view this website:
http://www.mathsisfun.com/geometry/interior-angles-polygons.html.

Finding the Area of a Hexagon